Question: Given $ m \angle BOC = 8x - 67$, $ m \angle AOB = 9x - 75$, and $ m \angle AOC = 96$, find $m\angle BOC$. $O$ $A$ $C$ $B$
From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {9x - 75} + {8x - 67} = {96}$ Combine like terms: $ 17x - 142 = 96$ Add $142$ to both sides: $ 17x = 238$ Divide both sides by $17$ to find $x$ $ x = 14$ Substitute $14$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 8({14}) - 67$ Simplify: $ {m\angle BOC = 112 - 67}$ So ${m\angle BOC = 45}$.